Improved approximations to distributions of the largest and the smallest latent roots of a wishart matrix

Summary Normalizing transformations of the largest and the smallest latent roots of a sample covariance matrix in a normal sample are obtained, when the corresponding population roots are simple. Using our results, confidence intervals for population roots may easily be constructed. Some numerical comparisons of the resulting approximations are made in a bivariate case, based on exact values of the probability integral of latent roots.     

Structural study of Si(1 1 1)-6 × 1-Ag surface using surface X-ray diffraction

The surface structure of Si(1 1 1)-6 × 1-Ag was investigated using surface X-ray diffraction techniques. By analyzing the CTR scattering intensities along 00 rod, the positions of the Ag and reconstructed Si atoms perpendicular to the surface were determined. The results agreed well with the HCC model proposed for a 3 × 1 structure induced by alkali-metals on a Si(1 1 1) substrate. The heights of the surface Ag and Si atoms did not move when the surface structure changed from Si(1 1 1)-√3 × √3-Ag to Si(1 1 1)-6 × 1-Ag by the desorption of the Ag atoms. From the GIXD measurement, the in-plane arrangement of the surface Ag atoms was determined. The results indicate that the Ag atoms move large distances at the phase transition between the 6 × 1 and 3 × 1 structures.     

Structure of the oxidized 4H-SiC(0 0 0 1)-3 × 3 surface

We have determined the structure of the 4H-SiC(0 0 0 1)-3 × 3 surface after exposure to small amounts of molecular oxygen at room temperature using surface X-ray diffraction. The 3 × 3 reconstruction remains until at least an exposure of 10,000 L, but the diffracted intensities change, indicating structural changes. Comparison of the Patterson maps of the clean and oxidized surface shows that the main changes occur at the Si tetramer on top of the 3 × 3 surface. Atomic positions for several models were fitted to the experimental data. A model in which oxygen atoms are inserted into the Si tetramer gives the best fit to the experimental data. The best-fit atomic positions agree well with those obtained using density functional calculations.     

Interdependence of Anion and Cation Exchanges in Calcium Hydroxyapatite: Pb(2+) and Cl(-)

The ion exchange of Pb(2+) and Cl(-) into calcium hydroxyapatite from aqueous solutions is studied at 293 K. Although the exchange of Cl(-) into CaHAp and PbHAp was not observed, in the presence of both Pb(2+) and Cl(-) in aqueous solution the exchange of both Pb(2+) and Cl(-) into CaHAp occurred, and, at least at intermediate concentrations of HCl, a proportionality between the sorbed quantities of these two ions was observed. The dissolution of CaHAp is shown to be dependent upon the pH, while the quantity of Pb(2+) exchanged into the solid is not a function of the proton content; consequently, the exchange is not primarily a dissolution-precipitation process. Copyright 1999 Academic Press.     

Synthesis,Structures, and Properties of Highly Strained Cyclophenylene–Ethynylenes with Axial and Helical Chirality

Single and double cyclophenylene–ethynylenes (CPEs) with axial and helical chirality have been synthesized by the Sonogashira cross‐coupling of di‐ and tetraethynyl biphenyls with a U‐shaped prearomatic diiodoparaphenylene followed by reductive aromatization. X‐ray crystallographic analyses and DFT calculations revealed that the CPEs possess highly twisted bent structures. Bend angles on the edge of the paraphenylene units were close to the value of [5]cycloparaphenylene (CPP)—the smallest CPP to date. The double and single CPEs possessed stable chirality despite flexible biphenyl structures because of the high strain in the diethynyl–paraphenylene moiety. In both the single and double CPEs, orbital interactions along the biphenyl axis were observed by DFT calculations in LUMO and LUMO+2 of the single CPE and LUMO+1 of the double CPE, which likely cause lowering of these orbital energies. Concerning chiroptical properties: boosting of the g_abs value was observed in the biphenyl‐based double CPE, as well as the binaphthyl‐based single CPE, compared to the biphenyl‐based single CPE.     

DNA alkylation by pyrrole-imidazole seco-CBI conjugates with an indole linker: sequence-specific DNA alkylation with 10-base-pair recognition through heterodimer formation

The sequence-specific DNA alkylation by conjugates 4 and 5, which consist of N-methylpyrrole (Py)-N-methylimidazole (Im) polyamides and 1-(chloromethyl)-5-hydroxy-1,2-dihydro-3H-benz[e]indole (seco-CBI) linked with an indole linker, was investigated in the absence or presence of partner Py-Im polyamide 6. High-resolution denaturing polyacrylamide gel electrophoresis revealed that conjugate 4 alkylates DNA at the sequences 5'-(A/T)GCCTA-3' through hairpin formation, and alkylates 5'-GGAAAGAAAA-3' through an extended binding mode. However, in the presence of partner Py-Im polyamide 6, conjugate 4 alkylates DNA at a completely different sequence, 5'-AGGTTGTCCA-3'. Alkylation of 4 in the presence of 6 was effectively inhibited by a competitor 7. Surface plasmon resonance (SPR) results indicated that conjugate 4 does not bind to 5'-AGGTTGTCCA-3', whereas 6 binds tightly to this sequence. The results suggest that alkylation proceeds through heterodimer formation, indicating that this is a general way to expand the recognition sequence for DNA alkylation by Py-Im seco-CBI conjugates.     

D-Fructose-6-phosphate aldolase-catalyzed one-pot synthesis of iminocyclitols

A one-pot chemoenzymatic method for the synthesis of a variety of new iminocyclitols from readily available, non-phosphorylated donor substrates has been developed. The method utilizes the recently discovered fructose-6-phosphate aldolase (FSA), which is functionally distinct from known aldolases in its tolerance of different donor substrates as well as acceptor substrates. Kinetic studies were performed with dihydroxyacetone (DHA), the presumed endogenous substrate for FSA, as well as hydroxy acetone (HA) and 1-hydroxy-2-butanone (HB) as donor substrates, in each case using glyceraldehyde-3-phosphate as acceptor substrate. Remarkably, FSA used the three donor substrates with equal efficiency, with kcat/KMvalues of 33, 75, and 20 M-1 s-1, respectively. This level of donor substrate tolerance is unprecedented for an aldolase. Furthermore, DHA, HA, and HB were accepted as donors in FSA-catalyzed aldol reactions with a variety of azido- and Cbz-amino aldehyde acceptors. The broad substrate tolerance of FSA and the ability to circumvent the need for phosphorylated substrates allowed for one-pot synthesis of a number of known and novel iminocyclitols in good yields, and in a very concise fashion. New iminocyclitols were assayed as inhibitors against a panel of glycosidases. Compounds 15 and 16 were specific alpha-mannosidase inhibitors, and 24 and 26 were potent and selective inhibitors of beta-N-acetylglucosaminidases in the submicromolar range. Facile access to these compounds makes them attractive core structures for further inhibitor optimization.     

Potent platelet-derived growth factor-beta receptor (PDGF-betaR) inhibitors: Synthesis and structure-activity relationships of 7-[3-(cyclohexylmethyl)ureido]-3-{1-methyl-1H-pyrrolo[2,3-b]pyridin-3-yl}quinoxalin-2(1H)-one derivatives

We found previously that 7-[3-(cyclohexylmethyl)ureido]-3-{1-methyl-1H-pyrrolo[2,3-b]pyridin-3-yl}quinoxalin-2(1H)-one (7d-6) has considerable potency as a PDGF inhibitor. This compound showed potent inhibitory activity in a PDGF-induced CPA (Cell Proliferation Assay) and APA (Auto-Phosphorylation Assay) (IC50 = 0.05 micromol/l in CPA, 0.03 micromol/l in APA). Therefore, we tried to develop a novel and effective PDGF-betaR inhibitor by optimizing a series of its derivatives. We found that trifluoroacetic acid (TFA)-catalyzed coupling of pyrrolo[2,3-b]pyridines with quinoxalin-2-ones proceeded efficiently under mild oxidation condition with manganese(IV) oxide (MnO2) in situ, so this method was applied to prepare a series of derivatives. Results of in vitro screening of newly synthesized derivatives identified compound 7d-9 as having potent (IC50 = 0.014 micromol/l in CPA, 0.007 micromol/l in APA) and selective [IC50 values against vascular endothelial growth factor receptor 2 (VEGFR2, kinase domain region, KDR), epidermal growth factor receptor (EGFR), c-Met (hepatocyte growth factor receptor) and insulin growth factor I receptor (IGF-IR)/IC50 against PDGFR were each >1000] inhibitory activity. Moreover, in this series of derivatives, 7b-2 showed potent inhibitory activity toward both PDGF- and VEGF-induced signaling (PDGFR: IC50 = 0.004 micromol/l in CPA, 0.0008 micromol/l in APA, KDR: IC50 = 0.008 micromol/l in APA). Herein we report a new and convenient synthetic method for this series of derivatives and its SAR study.     

Diastereoselective intramolecular acyl transfer of 5-(α-methylbenzyl)amino-1,3-dioxan-2-one to 4-hydroxymethyl-2-oxazolidinones

Intramolecular acyl transfer of (R)-5-(α-methylbenzyl)amino-1,3-dioxan-2-one (2) by treatment with DBU in CD₂Cl₂, CDCl₃, C₆D₆, CD₃CN, CD₃NO₂, DMSO-d₆, DMF, THF-d₈, ⁱPrOH, and ^tBuOH at room temperature afforded (4S,αR)-4-hydroxymethyl-3-α-methylbenzyl-2-oxazolidinone [(4S)-3] in moderate to quantitative yields with 58-94% de via an asymmetric desymmetrization process. Treatment of 2 with DBU and Cs₂CO₃ in MeOH and EtOH gave (4S)-3 and (4R)-3 without diastereoselectivities. Acidic treatment of 2 using HCO₂H, AcOH, EtCO₂H, ⁱPrCO₂H, ^tBuCO₂H, and C₆F₅OH in CDCl₃ gave (4S)-3 in moderate diastereoselectivities (26-52% de). First-order kinetics were observed in the reaction of 2 to (4S)-3 with DBU in CDCl₃ and THF-d₈.